A244727 a(n) = 7*n^3.

0, 7, 56, 189, 448, 875, 1512, 2401, 3584, 5103, 7000, 9317, 12096, 15379, 19208, 23625, 28672, 34391, 40824, 48013, 56000, 64827, 74536, 85169, 96768, 109375, 123032, 137781, 153664, 170723, 189000, 208537, 229376, 251559, 275128, 300125, 326592, 354571, 384104

Offset: 0

Author

Vincenzo Librandi, Jul 05 2014

Keywords

• nonn
• easy

Comments

After 0, subsequence of A038855.

Volume of a truncated square pyramid with base lengths n and 2n, and height 3n. - Wesley Ivan Hurt, Apr 05 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A038855.

Cf. similar sequences listed in A244725.

Programs

Magma

[7*n^3: n in [0..40]];

Magma

I:=[0,7,56,189]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]];

Maple

A244727:=n->7*n^3: seq(A244727(n), n=0..100); # Wesley Ivan Hurt, Apr 05 2016

Mathematica

Table[7 n^3, {n, 0, 40}] (* or *) CoefficientList[Series[7 x (1 + 4 x + x^2)/(1 - x)^4, {x, 0, 40}], x]
7 Range[0, 50]^3 (* Wesley Ivan Hurt, Apr 05 2016 *)
LinearRecurrence[{4,-6,4,-1},{0,7,56,189},40] (* Harvey P. Dale, Apr 04 2024 *)

Formula

G.f.: 7*x*(1 + 4*x + x^2)/(1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.

E.g.f.: 7*exp(x)*x*(1 + 3*x + x^2). - Stefano Spezia, May 09 2023